multiple different sized plots in same window in R?

Similar questions have been asked many times, for example here and here. However, all of the other answers I have seen so far don't really solve my problem.

I am trying to plot multiple different sized plots in the same window. I am working with tidygraph objects and using ggraph to create the plots. I tried using gridExtra and cowplots, however, I cant seem to get them to work as I want.

For example, to begin I create some data, turn them into tidygraph objects and put them together in a list, like so:

library(tidygraph)
library(ggraph)
library(cowplot)
library(gridExtra)


# create some data
edges  <- data.frame(from = c(1,1), to = c(2,3))
edges1 <- data.frame(from = c(1, 2, 2, 1, 5, 5), to = c(2, 3, 4, 5, 6, 7))
edges2 <- data.frame(from = c(1,2,2,1), to = c(2,3,4,5))

tg   <- tbl_graph(edges = edges)
tg_1 <- tbl_graph(edges = edges1)
tg_2 <- tbl_graph(edges = edges2)

myList <- list(tg, tg_1, tg_2)

Then I create a plotting function using ggraph and create a list of plots, like so:

# create plotting function
plotFun <- function(List, n) {
   plot <- ggraph(List, "partition") +
    geom_node_tile(aes(fill = "red"), size = 0.25) +
    scale_y_reverse() +
    theme_void() +
    theme(legend.position = "none")
}

# create list of all plots
allPlots <- lapply(myList, plotFun, n = length(myList))

So, in my example, I have 3 different plots... and I am trying to plot all 3 in the same window, but each plot has a different size. My desired output is shown in the image below...

What I was trying to do is have one plot "full-sized", the 2nd plot, 1/2 the size of the first plot, and the third plot 1/4 the size of the first plot. That would look something like:

NOTE: the image was made in photoshop, so the scales I mentioned above aren't exact in the image.

My ideas at an attempted solution were to use either gridExtra or cowplot... I have included some basic attempts, but they don't work... they seem to change the column or row size rather than the actual plot size:

Attemped Solutions

# ATTEMPED COWPLOT SOLUTION
plot_grid(plotlist = allPlots, align = "hv", ncol = 2, rel_heights = c(1, 1/2, 1/4), rel_widths = c(1, 1/2, 1/4))


# ATTEMPED GRIDEXTRA SOLUTION
grid.arrange(
  grobs = allPlots,
  widths = c(1, 0.5, 1/4),
  heights = c(1, 0.5, 1/4),
  layout_matrix = rbind(c(1, 2, 3))
)

EDIT -- fixed to shrink third chart per OP.

library(patchwork)
design <- c(         # we specify the top, left, bottom, and right
  area(1, 1, 4, 4),  # coordinates for each of the three plots
  area(1, 5, 2, 6),
  area(3, 5)
)
allPlots[[1]] +  allPlots[[2]] + allPlots[[3]] + 
  plot_layout(design = design)