I understand that unlike for ChIP-seq, with ATAC-seq MACS doesn't estimate the model, which means it doesn't determine distance 'd' between the tags and therefore it doesn't shift the tags by d/2 in 3´direction (and that is why with ATAC-seq the --nomodel --shift 0 parameters are set).

But if 'd' is not estimated then how can MACS slide a window of 2d across the genome to calculate peak enrichment?

Also, for ChIP-seq there is a control sample (input DNA or DNA pulled down with an unspecific antibody) that is used to calculate lambda local and determine peak enrichment. In ATAC-seq there isn't any control pulled down with unspecific antibody. What is that control in ATAC-seq?

MACS (for ChIP or ATAC) does not necessarily need a control. There is actually a section in the paper describing exactly the situation where no control is available. In this case, it determines the local lambda in certain windows. The paragraph starts with:

>  Therefore, instead of using a uniform λBG, estimated from the whole genome, MACS uses a dynamic parameter, λlocal, defined for each candidate peak as (...)

In the absence of a control, naively one would estimate the background level of the experiment in a uniform fashion. That means if you have, say 30mio reads and you randomly threw them onto the genome, then every base (given a certain fragment length of the library) would have a coverage of x. Still, the genome coverage is never uniform (you will most impressively see once you analyze your first WGS sample, it is really a hilly landscape) due to differences in chromatin structure, PCR/GC bias, local copy number alterations etc. So instead of a genome-wide λBG, MACS checks the vicinity of the peak centers (up to 10kb) to estimate how prone this genomic region is to accumulate reads. In my understanding, as a typical ChIPseq experiment produces sharp peaks, the local environment should be depleted for enriched signals. Therefore, notable readcounts in the vicinity are an indication of a local bias. As a result, the peak enrichment needs to be penalized (down-corrected), as the region itself is prone to accumulate enrichment, irrespective of the protein target.
