all these ICOs tokens offers to finance new startups are under ethereum technology?

Question

or they start their own blockchain on any new ICO?

If the answer is that they can be both, what are the advantages of every approach?

Thanks in advance

Answer 1

Possibly off-topic...

all these ICOs tokens offers to finance new startups are under ethereum technology?

Not all of them are on Ethereum.

Here's a count of the number of tokens - each potentially having had its own ICO - on different parent platforms (according to CoinMarketCap as of 19 Feb 2018):

Total token count:        611       
-----------------------------
Ethereum                  503
Waves                      27
BitShares                  19
Omni                       13
Counterparty                9
Qtum                        9
NEO                         8
Nxt                         5
Ubiq                        4
NEM                         3
Stellar                     3
Ethereum Classic            2
Ardor                       2
Burst                       2
NuBits                      1

or they start their own blockchain on any new ICO?

Some of them have their own blockchain, or claim that they will move to their own blockchain at some point in the future. You'll have to investigate specific cases to work out what their strategy is.

If the answer is that they can be both, what are the advantages of every approach?

Different people will have different opinions on this part.