How bitcoin network appends new block in its Block-chain Well, According to my research, After solving the cryptographic hash, when the multiple nodes broadcast the block at the same time as a suggestion to be the next block in the chain. Bitcoin network adds all those blocks to the chain.
Suppose three miners had successfully added blocks (a group of transactions). Means, now there are 3 chains. So, Now the next block will append which Block-chain 1st, 2nd or third? Please explain, How future blocks will append the Block-chain. Moreover, How the network will handle this situation?

Please let me know if my concept is wrong. I will appreciate your guidance. Thanks
The math makes it rare for boxes to be solved at the same time. However, Yes it's true. If more than one miner solves the cryptographic hash at the same time can add a block (a group of transactions) which as a result, leads to multiple branches. In this case, you simply build on the top of the first one you received.
Solution The tie gets broken when someone solved the next block. Because The general rule is that you always immediately switch to the longest branch available. The end result is that the blockchain quickly stabilizes.
So, the transactions of an ignored block of a small chain, go back to the unconfirmed transaction pool and be included in a later block.