local wallet has to be running on my desktop to receive payment?

[mightcoin]

does my wallet have to be running on my computer at the exact moment of payment to receive it?


Edited for clear wording

[some1]

does my wallet have to be online at the exact moment of payment to receive it?

absolutely not

[AmDD]

does my wallet have to be online at the exact moment of payment to receive it?

No. Actually the payment never gets sent to the wallet, the wallet just gives you access to the coins on the network.

[mightcoin]

does my wallet have to be online at the exact moment of payment to receive it?

No. Actually the payment never gets sent to the wallet, the wallet just gives you access to the coins on the network.

If the payment never gets sent to the my local wallet, does the amount leave the sender's wallet?

Or, does the network "remember" the payment, and the next time my local wallet is connected, the money is downloaded to my wallet? 
 

[torry28]

does my wallet have to be online at the exact moment of payment to receive it?

No. Actually the payment never gets sent to the wallet, the wallet just gives you access to the coins on the network.

The wallet informs you when you receive the coins though, but this info is available for everyone. It is public blockchain afterall

[gweedo]

does my wallet have to be online at the exact moment of payment to receive it?

No. Actually the payment never gets sent to the wallet, the wallet just gives you access to the coins on the network.

If the payment never gets sent to the my local wallet, does the amount leave the sender's wallet?

Or, does the network "remember" the payment, and the next time my local wallet is connected, the money is downloaded to my wallet?  

Bitcoin is a p2p network, so when someone sends a payment, they are just basically announcing to the blockchain and the miners they want to take this address and move the coins to this other address. And the miners do that for you. Then the blockchain is updated. No coins are stored in your wallet, only private keys that allow that transaction to happen, not the connection of the wallets.

[torry28]

does my wallet have to be online at the exact moment of payment to receive it?

No. Actually the payment never gets sent to the wallet, the wallet just gives you access to the coins on the network.

If the payment never gets sent to the my local wallet, does the amount leave the sender's wallet?

Or, does the network "remember" the payment, and the next time my local wallet is connected, the money is downloaded to my wallet? 

The info what address send Bitcoin to another Bitcoin address is publicly available, it is blockchain

You dont need download anything, you may check blockchain.info address ballance for example

[some1]

Bitcoins never go from one wallet to another.
They are in the network and here remain.

Your wallet is just a way to say: those are mine.

[Thopdpe]

does my wallet have to be online at the exact moment of payment to receive it?

No. Actually the payment never gets sent to the wallet, the wallet just gives you access to the coins on the network.

If the payment never gets sent to the my local wallet, does the amount leave the sender's wallet?

Or, does the network "remember" the payment, and the next time my local wallet is connected, the money is downloaded to my wallet? 
 

The bitcoin is never sent "to your wallet".

When someone creates a tx which sends bitcoin to your addresses, the tx is broadcasted to the network, and later included in a block.
Your wallet contains private keys which enable you to spend the bitcoin on those addresses.